✦ LIBER ✦

Addition Theorems for Finite Abelian Groups

✍ Scribed by W.D. Gao

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 202 KB
Volume: 53
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1089

No coin nor oath required. For personal study only.

✦ Synopsis

Let (a_{1}, \ldots, a_{k}) be a sequence of elements in an Abelian group of order (n) (repetition allowed). In this paper, we give two sufficient conditions such that an element (g \in G) can be written in the form (g=a_{i_{1}}+a_{i_{2}}+\cdots+a_{i_{n}}, 1 \leqslant i_{1}<i_{2}<\cdots<i_{n} \leqslant k), if and only if for every (b \in G, g) can be written in the form (g=\left(b+a_{j_{1}}\right)+\cdots+\left(b+a_{j_{k s} k_{2}}\right)). (1 \leqslant j_{1}<\cdots<j_{t b,} \leqslant k, 1 \leqslant l(b) \leqslant k). As an application of this result, we improve a result of Olson. 1995 Academic Press. Inc

📜 SIMILAR VOLUMES

Limit theorems on locally compact Abelia

Limit theorems on locally compact Abelian groups

✍ Mátyás Barczy; Alexander Bendikov; Gyula Pap 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 221 KB 👁 1 views

## Abstract We prove limit theorems for row sums of a rowwise independent infinitesimal array of random variables with values in a locally compact Abelian group. First we give a proof of Gaiser's theorem [4, Satz 1.3.6], since it does not have an easy access and it is not complete. This theorem giv

Algorithmic Methods for Finitely Generat

Algorithmic Methods for Finitely Generated Abelian Groups

✍ Henri Cohen; Francisco Diaz Y Diaz; Michel Olivier 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 357 KB

We describe algorithmic tools to compute with exact sequences of Abelian groups. Although simple in nature, these are essential for a number of applications such as the determination of the structure of (Z K /m) \* for an ideal m of a number field K, of ray class groups of number fields, and of cond

A Combinatorial Problem on Finite Abelia

A Combinatorial Problem on Finite Abelian Groups

✍ W.D. Gao 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 186 KB

In this paper the following theorem is proved. Let G be a finite Abelian group of order n. Then, n+D(G )&1 is the least integer m with the property that for any sequence of m elements a 1 , ..., a m in G, 0 can be written in the form 0= a 1 + } } } +a in with 1 i 1 < } } } <i n m, where D(G) is the

The Cross Number of Finite Abelian Group

The Cross Number of Finite Abelian Groups

✍ A. Geroldinger 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 119 KB

An Embedding Theorem for Abelian Categor

An Embedding Theorem for Abelian Categories

✍ P.N. Anh 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 307 KB

Circuits in cayley digraphs of finite ab

Circuits in cayley digraphs of finite abelian groups

✍ Anne Marie Wilkinson 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 290 KB

## Abstract We find all possible lengths of circuits in Cayley digraphs of two‐generated abelian groups over the two‐element generating sets and over certain three‐element generating sets.